Engineer who turned into a PM, here (now a Project Manager, same situation applies). I, too, found there was no upward career path as a software engineer, and thought a role switch would help. It doesn't. Same root cause: The pyramid gets very small towards the top, and companies' only advancement opportunities involve going up the pyramid. At some point, you find you're not going to advance unless your boss quits, and even if that happens, that one promotion will just as likely go to one of your 20 peers.
Thoughts on the switch? I decided to become a PM full-time after a couple of dev internships, thinking that given the pace of change in tech, it would be a better idea to spend time building people skills instead as those seemed to be more 'durable'.
After a couple of years, I've completely changed my mind. Though I've done well in my role, I find that it's hard to point to a concrete skill set (such as deep domain knowledge in some field), and the fact that the PM role varies so much across companies makes it difficult to transition.
It's a mixed bag. Product management and project management are broader roles that let you see the bigger picture, and let you interact with more people at your company. If you're a PM or PJM at a smallish (100-300 person) company, you'll know everyone in the company within your first year. So it's a good career move if you're more outgoing/extroverted. It's also nice to not have to constantly be running the "hot technology" treadmill to stay relevant. I can pick and choose what languages/frameworks to learn that I think will be most valuable, instead of having to dabble in everything because "Framework X is outdated--Everyone's using Framework Y now!"
Downside is you generally have to let go of direct control of what code goes into the products and let your talented engineers do it. My first few months as a PM I still wanted to commit code and had to stop myself. There is also far less demand for PMs and PJMs at tech companies. Everyone's hiring developers by the truckload, but PM positions are few and far between. The whole "it's easy to change jobs in Silicon Valley" thing only really applies to developers. Pay is also not as good as engineering (currently).
